Vehicle and method of advising a driver therein

ABSTRACT

A vehicle may include a driver interface and at least once controller operatively arranged with the interface. The at least one controller may be configured to categorize a driver&#39;s dynamic control of the vehicle by type, determine a target speed of a road curvature, and determine a speed of the vehicle. The at least one controller may be further configured to determine a threshold distance based on the type, determine a distance between the vehicle and the curvature, and generate an alert for the driver if the distance is less than the threshold and the speed is greater than the target.

BACKGROUND

Road curvatures and/or road intersections may present hazards forvehicle drivers.

SUMMARY

Advising a driver of a vehicle may include categorizing the driver'sdynamic control of the vehicle by type, determining a target speed of aroad curvature, determining a speed of the vehicle, determining adistance between the vehicle and the curvature, determining an alertcondition based on the type, target speed, speed, and a thresholddistance, and generating an alert in response to the alert condition.

Advising a driver may include categorizing the driver's dynamic controlof the vehicle by type, determining a threshold distance based on thetype, determining a distance between the vehicle and a roadintersection, and generating an alert for the driver if the distance isless than the threshold distance.

While example embodiments in accordance with the invention areillustrated and disclosed, such disclosure should not be construed tolimit the invention. It is anticipated that various modifications andalternative designs may be made without departing from the scope of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an embodiment of a vehicle control system.

FIG. 2 is a plot of example vehicle speed, traction and brakingprofiles.

FIGS. 3A through 3C are plots of example vehicle motion states of yawrate and sideslip angle.

FIGS. 4A through 4C are plots of example yawing, longitudinal, andsidesliping handling limit margins.

FIG. 5 is a plot of example vehicle speed, traction and brakingprofiles.

FIGS. 6A through 6C are plots of example vehicle motion states of yawrate and sideslip angle.

FIGS. 7A through 7C are plots of example yawing, longitudinal, andsidesliping handling limit margins.

FIG. 8 is a plot of example membership functions characterizing fourdriver categories based on handling risk factor.

FIGS. 9A, 10A and 11A are plots of example final handling limit marginsand risk.

FIGS. 9B, 10B and 11B are plots of example probabilities of driverstyle.

FIG. 12 is a plot of example determinants of smooth and abrupt drivingbehaviors.

FIGS. 13A and 13B are plots of example mean gap times for aggressive andcautious driving respectively.

FIGS. 14A and 14B are plots of example standard deviations ofaccelerator pedal rate for aggressive and cautious driving respectively.

FIGS. 15A and 15B are plots of example standard deviations of brakepedal rate for aggressive and cautious driving respectively.

FIGS. 16A and 16B are plots of example driver indices for aggressive andcautious driving respectively.

FIG. 17 is a plot of an example relative range, range-error andlongitudinal acceleration between a leading and following car foraggressive driving.

FIG. 18 is a plot of select example parameters characterizing theaggressive driving of FIG. 17.

FIG. 19 is a plot of an example relative range, range-error andlongitudinal acceleration between a leading and following car forcautious driving.

FIG. 20 is a plot of select example parameters characterizing thecautious driving of FIG. 19.

FIG. 21 is an x-y plot showing a portion of a curve passing throughthree points.

FIG. 22 is a schematic diagram of a vehicle approaching an example roadcurvature.

FIG. 23 is a block diagram of an embodiment of a vehicle.

DETAILED DESCRIPTION I. Introduction

An objective of existing vehicle electronic control systems is tofacilitate the driving task by identifying driver intent and aiding thedriver by controlling the vehicle to achieve the driver intent safely,robustly, and smoothly. The control effectiveness of electronic controlsystems may be significantly increased when the driver and theelectronic control system work together towards the same accidentavoidance goal and maximize the accident avoidance capability of thedriver-in-the-loop vehicle as a system. One approach to achieve this isto provide timely clear and transparent advisory information to a driversuch that a responsible driver can respond accordingly. Such advisoryinformation can be gathered or computed from sensors normally found on avehicle and used for implementing a bilateral closed-loop controlbetween the driver and the electronic control. The electronic controlfollows the driver intent and the driver responds to the advisoryinformation from the electronic control to modify his drive inputs (suchas dropping throttle, easing steering inputs, braking, etc.) In thisway, a seamless coordination between the driver and the electroniccontrol system is possible and is likely to minimize the effect ofpotential safety hazards due to driver errors.

Here, we consider, inter alia, warnings that are issued in advance ofviolating a speed or acceleration limit. This may be part of a clusterof warning functions that may be defined as an Intelligent PersonalMinder (IPM) system. Generally speaking, the intelligence computed forthe IPM system can be sent to warn or advise a driver through variousdevices including a haptic pedal, a haptic steering wheel, aheads-up-display, an audio warning device, a voice system, etc.

FIG. 1 depicts the interaction of an embodiment of an IPM system 10 withother components/subsystems 12 of a vehicle 14. The othercomponents/subsystems 12 may include vehicle sensors 16, 18 (e.g., a yawrate sensor, roll rate sensor, steering angle sensor, lateralacceleration sensor, longitudinal acceleration sensor, wheel speedsensor, brake pressure sensor, etc.), actuators 20 and one or morecontrollers 22. The one or more controllers 22 may include stabilitycontrol 24, arbitration logic 26 and other controllers/systems 28 (e.g.,anti-lock braking system, traction control system, yaw stabilitycontrol, roll stability control, etc.)

For any control system, the plant model may play a role in designing aneffective control strategy. Similarly, a driver model is important forgenerating effective and appropriate driver advisory signals. Hence,driving style characterization may be needed. We discuss methods ofidentifying a driver's characteristics based on his or her vehiclehandling capability, pattern used to actuate actuators, car-followingevents, etc. While driver modeling and driver behavior characterizationhave been studied (primarily off-line), we suggest an approach in whichthe driving behavior/style and/or the driving experience level may bededuced, for example, based on the frequency and duration of drivingclose to the handling limit, as well as other techniques. Such drivercharacterization information may be used in a variety of applications,some of which are discussed below.

II. A Brief Discussion of Vehicle Stability Controls

A vehicle's handling determines the vehicle's ability to corner andmaneuver. The vehicle needs to stick to the road with its four tirecontact patches in order to maximize its handling capability. A tirewhich exceeds its limit of adhesion is either spinning, skidding orsliding. A condition where one or more tires exceed their limits ofadhesion may be called a limit handling condition and the adhesion limitmay be called a handling limit. Once a tire reaches its handling limit,the average driver is usually no longer in control. In the so-calledundersteer case, the car under performs a driver's steering input, itsfront tires pass their handling limit, and the vehicle continues goingstraight regardless of the driver's steering request. In the so-calledoversteer case, the car over performs the driver's steering inputs, itsrear tires pass their handling limit, and the vehicle continuesspinning. For safety purposes, most vehicles are built to understeer attheir handling limits.

In order to compensate vehicle control in case a driver is unable tocontrol the vehicle at or beyond the handling limit, electronicstability control (ESC) systems are designed to redistribute tire forcesto generate a yawing moment that can effectively turn the vehicleconsistent with the driver's steering request. Namely, to control thevehicle to avoid understeer or oversteer conditions.

Since its debut in 1995, ESC systems have been implemented in variousplatforms. Phasing in during model year 2010 and achieving fullinstallation by model year 2012, Federal Motor Vehicle Safety Standard126 requires ESC systems on any new vehicle with a gross weight ratingbelow 10,000 lb. ESC systems may be implemented as an extension ofanti-lock braking systems (ABS) and all-speed traction control systems(TCS). They may provide the yaw and lateral stability assist to thevehicle dynamics centered around the driver's intent. It may alsoproportion brake pressure (above or below the driver applied pressure)to individual wheel(s) so as to generate an active yawing moment tocounteract the unexpected yaw and lateral sliding motions of thevehicle. This leads to enhanced steering control at the handling limitsfor any traction surface during braking, accelerating or coasting. Morespecifically, current ESC systems compare the driver's intended path tothe actual vehicle response which is inferred from onboard sensors. Ifthe vehicle's response is different from the intended path (eitherundersteering or oversteering), the ESC controller applies braking atselected wheel(s) and reduces engine torque in order to keep the vehicleon the intended path and to minimize loss of control of the vehicle.

A limit handling condition can be detected using data already existingin ESC systems, so new sensors may not be required. Consider, forexample, a vehicle equipped with an ESC system using a yaw rate sensor,a steering wheel sensor, a lateral accelerometer, a set of wheel speedsensors, a master cylinder brake pressure sensor, a longitudinalaccelerometer, etc. The vehicle motion variables are defined in thecoordinate systems as defined in ISO-8855, where a frame fixed on thevehicle body has its vertical axis up, longitudinal axis along thelongitudinal direction of the vehicle body, and a lateral axis pointedfrom the passenger side to the driver side.

Generally speaking, vehicle level feedback controls can be computed fromindividual motion variables such as yaw rate, sideslip angle, or theircombination together with arbitrations with the other control commandssuch as driver braking, engine torque request, ABS and TCS. Vehiclelevel control commands are discussed in the following.

The well-known bicycle model captures the vehicle dynamics, its yaw rateω_(z) along the vertical axis of the vehicle body and its sideslip angleβ_(r) defined at its rear axle, and obeys the following equations

I _(z){dot over (ω)}_(z) =−b _(f) c _(f)(β_(r) +bω _(zt) v _(x) ⁻¹−δ)+b_(r) c _(r)β_(r) +M _(z)

M({dot over (v)} _(x)β_(r) +v _(x){dot over (β)}_(r) +b _(r){dot over(ω)}_(z)+ω_(z) v _(x))=−c _(f)(β_(r) +bω _(z) v _(x) ⁻¹−δ)−c_(r)β_(r)  (1)

where v_(x) is the vehicle's travel speed, M and I_(z) are the totalmass and the yaw moment of inertia of the vehicle, c_(f) and c_(r) arethe cornering stiffness of the front and rear tires, b_(f) and b_(r) arethe distances from the center of gravity of the vehicle to the front andrear axles, b=b_(f)+b_(r), M_(z) is the active moment applied to thevehicle, and δ is the front wheel steering angle.

A target yaw rate ω_(zt) and a target sideslip angle β_(rt) used toreflect the driver's steering intent can be calculated from (1) usingthe measured steering wheel angle δ and the estimated travel velocityv_(x) as the inputs. In such a computation, we assume that the vehicleis driven on a road of normal surface condition (e.g., high frictionlevel with nominal cornering stiffness c_(f) and c_(r)). Signalconditioning, filtering and nonlinear corrections for steady state limitcornering may also be performed in order to fine tune the target yawrate and the target sideslip angle. These calculated target valuescharacterize the driver's intended path on a normal road surface.

The yaw rate feedback controller is essentially a feedback controllercomputed from the yaw error (the difference between the measured yawrate and the target yaw rate). If the vehicle is turning left andω_(z)≧ω_(zt)+ω_(zdbos) (where ω_(zdbos) is a time varying deadband), orthe vehicle is turning right and ω_(z)≦ω_(zt)−ω_(zdbos), the vehicle isoversteering and activating the oversteer control function in ESC. Forinstance, the active torque request (applied to the vehicle for reducingthe oversteer tendency) might be computed as in the following

during a left turn: =min (0,−k _(os)(ω_(z)−ω_(zt)−ω_(zdbos)))  (2)

during a right turn: =max (0,−k _(os)(ω_(z)−ω_(zt)+ω_(zdbos)))

where k_(os) is a speed dependent gain which might be defined as in thefollowing

$\begin{matrix}{k_{os} = {k_{0} + {\left( {v_{x} - v_{xdbl}} \right)\frac{k_{dbu} - k_{dbl}}{v_{xdbu} - v_{xdbl}}}}} & (3)\end{matrix}$

with parameters k₀, k_(dbl), k_(dbu), v_(xdbl), v_(xdbu) being tunable.

If ω_(z)≦ω_(z)−ω_(zdbus) (where ω_(zdbus) is a time varying deadband)when the vehicle is turning left or ω_(z)≧ω_(z)+ω_(zdbus) when thevehicle is turning right, the understeer control function in ESC isactivated. The active torque request can be computed as in the following

during a left turn: M _(z)=max(0,−k _(us)(ω_(z)−ω_(zt)+ω_(zdbus)))

during a right turn: M _(z)=min(0,−k _(us)(ω_(z)−ω_(zt)−ω_(zdbus)))  (4)

where k_(us) is a tunable parameter.

The sideslip angle controller is a supplementary feedback controller tothe aforementioned oversteer yaw feedback controller. It compares thesideslip angle estimation β_(r) to the target sideslip angle β_(rt). Ifthe difference exceeds a threshold β_(rdb), the sideslip angle feedbackcontrol is activated. For instance, the active torque request iscalculated as in the following

during a left turn: β_(r)≧0:M _(z)=min(0,k _(ss)(β_(r) −B _(rt) −B_(rdb))−k _(sscmp){dot over (β)}_(rcmp))

during a right turn: β_(r)≧0:M _(z)=max(0,k _(ss)(β−B _(rt) −B _(rdb))−k_(sscmp){dot over (β)}_(rcmp))  (5)

where k_(ss) and k_(sscmp) are tunable parameters and {dot over(β)}_(rcmp) is a compensated time derivative of the sideslip angle.

Other feedback control terms based on variables such as yaw accelerationand sideslip gradient can be similarly generated. When the dominantvehicle motion variable is either the yaw rate or the sideslip angle,the aforementioned active torque can be directly used to determine thenecessary control wheel(s) and the amount of brake pressures to be sentto corresponding control wheel(s). If the vehicle dynamics are dominatedby multiple motion variables, control arbitration and prioritizationwill be conducted. The final arbitrated active torque is then used todetermine the final control wheel(s) and the corresponding brakepressure(s). For example, during an oversteer event, the front outsidewheel is selected as the control wheel, while during an understeerevent, the rear inside wheel is selected as the control wheel. During alarge side-slipping case, the front outside wheel is always selected asthe control wheel. When both the side slipping and oversteer yawinghappen simultaneously, the amount of brake pressure may be computed byintegrating both yaw error and the sideslip angle control commands.

Besides the above cases where the handling limit is exceeded due to thedriver's steering maneuvers, a vehicle can reach its limit handlingcondition in its longitudinal motion direction. For example, braking ona snowy and icy road can lead to locked wheels, which increases thestopping distance of the vehicle. Open throttling on a similar road cancause the drive wheels to spin without moving the vehicle forward. Forthis reason, the handling limit may also be used for these non-steeringdriving conditions. That is, the conditions where the tire longitudinalbraking or driving forces reach their peak values may also be includedin a definition of the handling limit.

The ABS function monitors the rotational motion of the individual wheelsin relation to the vehicle's travel velocity, which can be characterizedby the longitudinal slip ratios λ_(i), with i=1, 2, 3, 4 for thefront-left, front-right, rear-left and rear-right wheels, computed as inthe following

$\begin{matrix}{{\lambda_{1} = {\frac{\kappa_{1}\omega_{1}}{\max \begin{pmatrix}{{\left( {v_{x} + {\omega_{z}t_{f}}} \right){\cos (\delta)}} +} \\{{\left( {v_{y} + {\omega_{z}b_{f}}} \right){\sin (\delta)}},v_{\min}}\end{pmatrix}} - 1}}{\lambda_{2} = {\frac{\kappa_{2}\omega_{2}}{\max \begin{pmatrix}{{\left( {v_{x} + {\omega_{z}t_{f}}} \right){\cos (\delta)}} +} \\{{\left( {v_{y} + {\omega_{z}b_{f}}} \right){\sin (\delta)}},v_{\min}}\end{pmatrix}} - 1}}{{\lambda_{3} = {\frac{\kappa_{3}\omega_{3}}{\max \left( {{v_{x} - {\omega_{z}t_{r}}},v_{\min}} \right)} - 1}},{\lambda_{4} = {\frac{\kappa_{4}\omega_{4}}{\max \left( {{v_{x} + {\omega_{z}t_{r}}},v_{\min}} \right)} - 1}}}} & (6)\end{matrix}$

where t_(f) and t_(r) are the half tracks for the front and rear axles,ω_(l) is the i^(th) wheel speed sensor output, κ_(i) is the i^(th) wheelspeed scaling factor, v_(y) is the lateral velocity of the vehicle atits c.g. location, and v_(min) is a preset parameter reflecting theallowable minimum longitudinal speed. Notice that (6) is only valid whenthe vehicle is not in the reverse driving mode. When the driverinitiated braking generates too much slip (e.g., −λ_(i)≧λ_(bp)=20%) at awheel, the ABS module will release the brake pressure at that wheel.Similarly, during a large throttle application causing a large slip onthe i^(th) driven wheel, the TCS module will request engine torquereduction and/or brake pressure applied to the opposite wheel at thesame axle. Consequently, ABS or TCS activations can be predicted bymonitoring how close λ_(i)s are from λ_(bp) and λ_(tp).

III. Handling Limit Driving Style Characterization

While the aforementioned ESC (including ABS and TCS) is effective inachieving its safety goal, further enhancement is still possible. Forexample, augmentation of ESC systems may be desirable for roll stabilitycontrol. The appropriate correction which ESC tries to make, however,may be counteracted by the driver or ambient conditions. A speedingvehicle, whose tire forces go far beyond the traction capability of theroad and the tires, might not be able to avoid an understeer accidenteven with ESC intervention.

We introduce an integration of the driver and ESC system such that theymay work cooperatively towards an enhanced control performance of thedriver-in-the-loop system. In certain embodiments, the proposed HandlingLimit Minder (HLM) determines how close the current driving condition isto the handling limit.

Generally speaking, accurate determination of the handling limitconditions would involve direct measurements of road and tirecharacteristics or very intensive information from many relatedvariables if direct measurements are not available. Currently, both ofthese methods are not mature enough for real-time implementation.

Due to their feedback feature, ESC systems may be configured todetermine the potential limit handling conditions through monitoring themotion variables of a vehicle such as those described in the lastsection. When the motion variables deviate from their reference valuesby a certain amount (e.g., beyond certain deadbands), the ESC systemsmay start to compute differential braking control command(s) anddetermine control wheel(s). The corresponding brake pressure(s) is thensent to the control wheel(s) to stabilize the vehicle. The startingpoint of the ESC activation can be thought of as the beginning of thehandling limit.

More specifically, we may define a relative handling limit margin h_(x)as in the following

$\begin{matrix}{h_{x} = \left\{ \begin{matrix}\frac{\overset{\_}{x} - x}{\overset{\_}{x}} & {{{if}\mspace{14mu} 0} \leq x \leq \overset{\_}{x}} \\\frac{x - \underset{\_}{x}}{\underset{\_}{x}} & {{{if}\mspace{14mu} \underset{\_}{x}} \leq x < 0} \\0 & {otherwise}\end{matrix} \right.} & (8)\end{matrix}$

where x is the deviation of a motion variable from its reference valueand [x, x] defines the deadband interval within which x falls withoutinitiating the ESC, ABS or TCS. x can be any of the control variablesdefined in the last section (or any other suitable control variable).

The benefit of h_(x) defined in (8) is that the driving condition can bequantitatively characterized into different categories. For instance,when h_(x)≦10%, the driving condition may be categorized as a red zonecondition where the driver needs to have special attention or take somespecial actions (e.g., slowing down the vehicle); when 10%<h_(x)<40%,the driving condition may be categorized as a yellow zone conditionwhich needs some level of special attention from the driver; when40%<h_(x)≦100%, the driving condition may be characterized as a normalcondition. In the normal condition, the driver need only to maintain hisnormal driving attention. Of course, other ranges may also be used.

Various audible and/or visual warnings may be activated to alert adriver about the handling limit margin. When h_(x)≦10% for example, awarning light/haptic device may activate to inform the driver that theyneed to slow down. Alternatively, a voice enabled display system mayinstruct the driver to take particular action. When 10%<h_(x)<40%, anaudible tone or display may inform the driver that they are approachingunstable driving conditions, etc.

More specifically, let us use the control variables computed in the lastsection to discuss the computation of h_(x)s. The vehicle's yaw handlinglimit margin during oversteer situations h_(OS) (where ω_(z)>ω_(zt) whenthe vehicle is turning to the left and ω_(z)>ω_(zt) when the vehicle isturning to the right) can be computed from (8) by setting x=ω_(z)−ω_(zt)and x=ω_(zdbos)=−x, where ω_(zdbos) is the oversteer yaw rate deadbandas defined in (2).

Similarly, the vehicle's yaw handling limit h_(US) for understeersituations can be computed from (8) by setting x=ω_(z)−ω_(zt) andx=ω_(zdbus)=−x, where ω_(zdbus) is the understeer yaw rate deadband asdefined in (4). Notice that the aforementioned deadbands might befunctions of the vehicle speed, the magnitude of the target yaw rate,the magnitude of the measured yaw rate, etc. The deadbands for theundersteer situation (x<0) and the oversteer situation (x>0) aredifferent and they are tunable parameters.

The vehicle's sideslip handling limit margin h_(SSRA) can be computedfrom (8) by setting x=β_(r)−β_(rt) and x=β_(rdb)=−x.

The longitudinal handling limits of the vehicle involve the conditionswhen either the driving or braking force of the tires approach thehandling limit. The traction control handling limit margin for thei^(th) driven wheel h_(TCS) _(i) can be computed from (8) by settingx=λ_(i), x=0, and xλ_(tb). The ABS handling limit margin for the i^(th)wheel h_(ABS) _(i) can also be computed from (8) by setting x=λ_(i),x=λ_(bp), and x=0. The final traction and braking handling limit marginsmay be defined as

$\begin{matrix}{{h_{ABS} = {\min\limits_{i \in {\{{1,2,3,4}\}}}h_{{ABS}_{i}}}},{h_{TCS} = {\min\limits_{i \in {\{{1,2,3,4}\}}}h_{{TCS}_{i}}}}} & (9)\end{matrix}$

Notice that further screening conditions may be used in computing theaforementioned handling limit margins. For instance, one of thefollowing or the combination of some of the following conditions mightbe used to set the handling limit margin as 0: a magnitude of the targetyaw rate is beyond a certain threshold; a magnitude of the measured yawrate is greater than a certain threshold; a driver's steering inputexceeds a certain threshold; or, extreme conditions such as thevehicle's cornering acceleration is greater than 0.5 g, the vehicle'sdeceleration is greater than 0.7 g, the vehicle is driven at a speedbeyond a threshold (e.g., 100 mph), etc.

In order to test the aforementioned handling limit margin computationsand verify their effectiveness with respect to known driving conditions,a vehicle equipped with a research ESC system developed at Ford MotorCompany was used to conduct vehicle testing.

For the driving condition profiled by the vehicle speed, throttling, andbraking depicted in FIG. 2, the measured and computed vehicle motionvariables are shown in FIGS. 3A through 3C. The corresponding individualhandling limit margins h_(US), h_(OS), h_(TCS), h_(ABS), and h_(SSRA)are shown in FIGS. 4A through 4 c. This test was conducted as a freeform slalom on a snow pad with all ESC computations running. The brakepressure apply was turned off in order for the vehicle to approach thetrue limit handling condition.

For another test, the vehicle was driven on a road surface with highfriction level. The vehicle speed, traction and braking profiles forthis test are depicted in FIG. 5. The vehicle motion states are shown inFIGS. 6A through 6C. The corresponding individual handling limit marginsh_(OS), h_(US), h_(TCS), h_(ABS), h_(SSRA) are shown in FIGS. 7A and 7B.

An envelope variable of all the individual handling limit margins isdefined as

h_(env)=min{h_(OS),h_(US),h_(TCS),h_(ABS),h_(SSRA)}  (10)

Considering that sudden changes in the envelope handling limit marginmight be due to signal noises, a low-pass filter F(z) is used to smoothh_(env) so as to obtain the final handling limit margin

h=F(z)h _(env)  (11)

For the vehicle test data shown on FIG. 2 and FIGS. 3A through 3C, thefinal handling limit margin is depicted in FIG. 9A, while for thevehicle test data shown on FIG. 5 and FIGS. 6A through 6C, the finalhandling limit margin is depicted in FIG. 10A.

We may now use the final handling limit margin computed in (11) tocharacterize vehicle handling related driving conditions and drivingstyle. We introduce the concept of a Handling Risk Factor (HRF) as themeasure of how a driving condition is related to the handling limit. Thehandling risk factor r is defined as the complement of the finalhandling limit margin h, i.e.,

r=1−h  (12)

The handling risk factor is minimal (r=0) when the final handling limitmargin h is maximal (h=1) and vice versa. The HRF may be further used todevelop a probabilistic model describing different categories of drivingstyles which are reflected by the current driving conditions withrespect to the handling limit.

Generally speaking, a cautious driver usually drives without frequentaggressiveness, i.e., fast changes of steering, speed and acceleration.Hence, it is reasonable to characterize a cautious driver as one whoconstantly avoids using extreme driving inputs and getting close to themaximal handling risk. An average driver likely exhibits a higher levelof HRF than a cautious driver. An expert driver might be more skilful incontrolling the vehicle, i.e., he can drive with a relatively high levelof HRF for a long duration without having the vehicle pass the maximalhandling limit. A reckless driver exhibits a careless handling behaviorwhich is unpredictable and could induce fast changes. The recklessdriver is expected to drive with a handling risk factor that mightapproach the maximum (r=1) very briefly from time to time, thus causingfrequent triggering of the related safety systems (e.g., ABS, TCS, ESC).

Notice that the difference between the expert driver and the recklessdriver is that the former can hold a driving condition at a relativelyhigh HRF level for long duration, while the latter can only hold at thesimilar level for a short duration before causing the vehicle to passthe maximal handling limit due to the driver's poor control capability.Since the handling risk factor ranges defining, for example, cautious,average, expert and reckless driving behavior (with respect to the limithandling conditions) may not be well defined, we use fuzzy subsets toquantify the four categories of drivers. We further evaluate thosecategories probabilistically based on a specific driver style. The fuzzysubsets associated with the categories of cautious, average, expert andreckless drivers may be described by the following membership functions

μ_(c)(r),μ_(e)(r),μ_(a)(r),μ_(r)(r)

defined over the HRF universe [0, 1]. FIG. 8 shows the relationshipbetween the degrees of membership for each of those categories and theHRF.

The membership functions in FIG. 8 can be assigned to any event that isrepresented by a specific HRF with value r_(k) using a four dimensionalvector

D _(k)=[μ_(c)(r _(k))μ_(e)(r _(k))μ_(a)(r _(k))μ_(r)(r _(k))]^(T)

of its degree of membership to each of the four example categories:cautious, average, expert and reckless. For example, a HRF valuer_(k)=0.4 (corresponding to handling limit margin value h_(k)=0.6) willtranslate to the degrees of membership to the cautious, average, expertand reckless categories

μ_(c)(0.4)=0.46,μ_(e)(0.4)=0.85

μ_(a)(0.4)=0.09,μ_(r)(0.4)=0.22

The membership grades encode the possibilities that the eventcharacterized by a HRF with value r=0.4 (or the handling limit marginh=0.6) might be associated with any of the four example partitions. Thevector of membership values d_(k) makes the association between a singledriving event and the possible driver characterization with respect tothe HRF of that event. In order to characterize the long term behaviorof the driver, we need a probabilistic interpretation of thepossibilities that are generated by multiple events. By adding themembership values for each event, we essentially aggregate the overallpossibilities that a specific driver can be categorized as cautious,average, expert and reckless, i.e., the vector

$\begin{matrix}{d^{*} = {\sum\limits_{k = 1}^{N}\; \left\lbrack {{\mu_{c}\left( r_{k} \right)}{\mu_{e}\left( r_{k} \right)}{\mu_{r}\left( r_{k} \right)}} \right\rbrack^{T}}} & (13)\end{matrix}$

where N is the number of samples. The aggregated possibilities can beconsidered as frequencies (sometimes referred to as fuzzy frequencies)since they reveal how frequently and to what degree the HRFs for themultiple events can be cascaded to the four example categories. Thealternative to aggregating the possibilities, i.e., adding themembership functions, is to add 1 if the specific membership gradeμ_(i)(r_(k)),iε{c,a,e,r} is greater than a prescribed threshold value,e.g., 0.8, or 0 otherwise, resulting in calculating the conventionalfrequency of the four example categories. From the aggregatedpossibilities, we can calculate the probabilities of the cautious,average, expert and reckless driver style

$\begin{matrix}{p_{i} = {d_{i}^{*}\left( {\sum\limits_{j \in {\{{c,a,e,r}\}}}\; d_{j}^{*}} \right)}^{- 1}} & (14)\end{matrix}$

where iε{c,a,e,r}. The probabilities are calculated from the aggregatedpossibilities (fuzzy frequencies) and can be considered fuzzyprobabilities. The reason for the fuzziness here is the lack ofcertainty in characterizing the relationship between the four examplecategories and the HRF. For the special case of crisply definedcategories (represented by intervals rather than fuzzy subsets), thepossibilities transform to Boolean values, their aggregated valuesbecome frequencies, and consequently the fuzzy probabilities aretranslated to conventional probabilities.

The most likely driver category i* is the one that is characterized withthe highest probability, i.e.,

$\begin{matrix}{i^{*} = {\arg\limits_{i \in {\{{c,a,e,r}\}}}{\max \left( p_{i} \right)}}} & (15)\end{matrix}$

The frequencies based calculation of the probabilities can be expressedin terms of the average frequencies

$\begin{matrix}{p_{i} = {d_{i}^{*}/{N\left( {\sum\limits_{j \in {\{{c,a,e,r}\}}}\; {d_{j}^{*}/N}} \right)}^{- 1}}} & (16)\end{matrix}$

Alternatively, it can be expressed through the exponentially weightedaverage frequencies where the higher weights are assigned to thepossibilities that are associated with the most recent events.Numerically, the process of generating a weighted average with higherweights corresponding to the recent observation can be accomplished byapplying a low pass filter implementing the exponential smoothingalgorithm in the time domain

d* _(new)=(1−α)d* _(old) +αd _(k) =d* _(old)+α(d _(k) −d* _(old))  (17)

where the constant forgetting factor 0<α≦1 controls the rate of updatingthe mean d* by assigning a set of exponentially decreasing weights tothe older observations. For a constant forgetting factor α, expression(17) recursively generates a vector of positive weights

W=└(1−α)^(k)α(1−α)^(k−1)α(1−α)^(k−2) . . . α┘  (18)

with a unit sum. Vector W delineates a weighted average type aggregatingoperator with exponentially decreasing weights that are parameterized bythe forgetting factor α. Parameter α defines the memory depth (thelength of the moving window) of the weighted averaging aggregatingoperator. Therefore, the filtered value d* of the membership gradevector in (17) represents the weighted averages of the individualpossibilities over the weights W. Since all of the aggregatedpossibilities are calculated over the same moving window of lengthK_(α)=1/α, we can consider them as representations of the frequencies ofthe associations with each of the four concepts. Weighted average (17)is calculated over the events with indexes belonging to a soft interval

sε{k−K_(α)+1,k]  (19)

where symbol { indicates a soft lower bound that includes values withlower indexes than (k−K_(α)) with relatively low contribution.Consequently, the aggregated possibilities that form the vector d* canbe converted to probabilities according to expression (14).

In certain embodiments, a may be selectable so that a characterizationfor a desired period of time is achieved. For example, a user may supplyinput related to α such that every half hour, a characterization ismade. Other scenarios are also possible.

For the vehicle testing depicted by FIGS. 2, 3A through 3C and 4Athrough 4C, the individual p_(i)'s are shown on FIG. 9B indicating thatfor most of the driving, the driver exhibited a reckless drivingbehavior, which is consistent with the large value of the sideslip anglein FIG. 3C (peak magnitude of the sideslip angle exceeds 10 degrees).For vehicle testing depicted by FIGS. 5 through 7C, the individualp_(i)'s are shown in FIG. 10B, indicating that the driver initiallyexhibited an average driver behavior and then transitioned to a recklessdriver behavior.

The calculated probabilities define the most likely HRF basedcharacterization of a driver for the time window that is specified bythe forgetting factor α. By modifying the moving window, we can learnand summarize the long and short term characterization for a specificdriver based on the HRF.

In order to predict the impact of the changes in HRF on the driver'scharacterization, we introduce the notion of transitional probabilities.The Markov model P probabilistically describes the set of transitionsbetween the current and the predicted value of the driver category:

$\begin{matrix}\; & \left. {p_{j}\left( {k + 1} \right)}\rightarrow \right. \\{p_{i}(k)} & \begin{matrix}p_{11} & p_{12} & p_{13} & p_{14} \\p_{21} & p_{22} & p_{23} & p_{24} \\p_{31} & p_{32} & p_{33} & p_{34} \\p_{41} & p_{42} & p_{43} & p_{44}\end{matrix}\end{matrix}$

where p_(ij) is the probability of switching from category i at time kto category j at time k+1, and p_(ii)=max(p_(i)) is the probability thatis associated with the dominating category i at time k, i, jε{c,a,e,r}.The transitional probabilities p_(ij) are derived from the transitionalaggregated possibilities that are updated only if i=arg max(p_(l)) attime k and j=arg max(p_(l)), lε{c,a,e,r}.

$\begin{matrix}{d_{{if},\; {new}}^{*} = \begin{Bmatrix}{{\left( {1 - \alpha} \right)d_{{if},\; {old}}^{*}} + {\alpha \; d_{i,k}}} & {{{if}\mspace{14mu} j} = {\arg\limits_{l \in {\{{c,a,e,r}\}}}{\max \left( p_{l} \right)}}} \\{\left( {1 - \alpha} \right)d_{{if},\; {old}}^{*}} & {otherwise}\end{Bmatrix}} & (20)\end{matrix}$

The transitional probabilities are then calculated by converting theaggregated transitional possibilities to the probabilities. The maximaltransitional probability p_(ij) determines the transition from categoryi to category j as the most likely transition.

FIGS. 11A and 11B use a driving vehicle test to verify long term drivingbehavior characterization. The driver generally shows a cautious drivingstyle (which could be a novice, average or expert driver). At around 190seconds, the vehicle was turned with some degree of aggressiveness whichcan be seen from the peak at the HRF plot, and the driving styletransitioned to the average category. Since no major HRF events werefurther identified, this category was carried out for the rest of thedriving cycle in conjunction with the concept of the long termcharacterization.

As mentioned above, various audible and/or visual warnings may beactivated to alert a driver about the handling limit margin. The marginthresholds that define whether (and/or what type) of warning is to beissued may be altered (or suspended) based on the drivercharacterization. For example, if it is determined that the driver is anexpert driver, the warning threshold may be reduced from h_(x)≦10% toh_(x)≦2%, or the warnings regarding the handling limit margin may besuspended (an expert driver may not need the warnings).

IV. Unsupervised Driving Style Characterization

During a normal driving maneuver, a driver's long term longitudinalvehicle control may be used to determine driving behavior regardless ofthe vehicle's dynamic response. For instance, a driver may exhibit aspecific longitudinal control pattern during driving on a highway for along period of time. His pattern of acceleration pedal activation can besmooth or abrupt even in the absence of emergency conditions. Thevariability of the pedal and its rate change can be used todifferentiate between smooth and abrupt application. Such a smooth orabrupt application exhibits strong correlation with fuel economy andacceleration performance when driving conditions are unconstrained.Identifying such driving behaviors can be used, for example, toimplement a fuel economy advisor.

Anomaly detection can be used to estimate major changes in the overallvariability of the control actions indicating changes in correspondingbehaviors. Anomaly detection is a technique that puts a major emphasison the continuous monitoring, machine learning, and unsupervisedclassification to identify a trend of departure from a normal behaviorand predict potential significant change. The determinant of thecovariance matrix of the population of a driver's actions may be used asa measure of the generalized variance (spread) of the population, andhence as an indicator for a change in the driver's behavior.

The feature space of driving torque request τ_(d) and its derivative isspanned by the vector y=[τ_(d){dot over (τ)}_(d)]. The determinant D ofthe covariance matrix of the population can be recursively calculated as

D _(k+1)=(1−α)^(k−1) D _(k)(1−α+(y _(k) −v _(k))Q _(k)(y _(k) −v_(k))^(T))  (21)

with

v _(k+1)=(1−α)v _(k) +αy _(k)

Q _(k+1)=(I−G _(k)(y _(k) −v _(k)))Q _(k)(1−α)⁻¹

G _(k+1) =Q _(k)(y _(k) −v _(k))^(T)α(1−α+α(y _(k) −v _(k))Q _(k)(y _(k)−v _(k))^(T))⁻¹  (22)

where v_(k) is a filtered version of y_(k), Q_(k) is the estimatedinverse covariance matrix, and α is a constant which reflects theforgetting factor related to the filter memory depth. D_(k) thuscomputed in (21) has initial means and standard deviations for abruptand smooth type behaviors. The instantaneous behavior is classified asabrupt if its value is higher than a control limit l_(abrupt) and isclassified as smooth if its value is lower than a control limitu_(smooth). l_(abrupt) and u_(smooth) are defined as

l _(abrupt)=μ_(abrupt)−3σ_(abrupt) ,u _(smooth)=μ_(smooth)+3σ_(smooth)

where μ_(abrupt) and σ_(abrupt) are the mean and standard deviation ofthe abrupt behavior class. μ_(smooth) and σ_(smooth) are similarlydefined for the smooth behavior class. If the current behavior isclassified as either abrupt or smooth, the corresponding mean andstandard deviation of the matching behavior are recursively updated

w _(k+1)=(1−β)w _(k) +βD _(k+1)

H _(k+1)=(1−β)H _(k)+(β−β²)(D _(k+1) −w _(k))^(T)(D _(k+1) −w _(k))

σ_(k+1)=(H _(k+1))^(1/2)  (23)

where w and H are the estimated mean and variance, and β is anotherforgetting factor.

FIG. 12 shows the determinant of the covariance matrix from the vectorof acceleration pedal position and its rate change for 8 runs of vehicletests. The 4 runs with solid lines of determinant were for abruptacceleration pedal applications. These determinants show a large value,for example, greater than 7. The 4 runs with dotted lines of determinantwere for smooth acceleration pedal applications. These determinants showa small value, for example, less than 4. Hence, the size of thedeterminant reveals the unique informative patterns which can be used todistinguish smooth driving behavior from abrupt driving behavior.

Since interactions between the driver and the driving environmentinclude frequent vehicle stops with varied durations, suspension of thecontinual updating may be required to prevent numerical problems duringrecursive computation. The following suspension conditions may be used:(i) If vehicle speed is less than 1 mph, vehicle speed and accelerationrelated recursive calculations are suspended. (ii) If the acceleratorpedal position is less than 1%, pedal related recursive calculations aresuspended.

Although the above deviation focuses on the acceleration pedal, it canbe easily applied to the braking case. Since sudden aggressive brakingcan happen during emergency situations (which are not necessarilyindicative of the driver's general behavior), quasi-steady state drivingwhere braking is not at its extreme may be used for computationalscreening.

During transient acceleration and deceleration, certain wheels of thevehicle may experience large longitudinal slip, and the tirelongitudinal forces of those wheels may reach their peak values. Suchconditions can be identified through monitoring the rotational motion ofthe individual wheels in relation to the vehicle's travel velocity, andconsequently the driver behavior during transient maneuvers can bedetermined as discussed above.

V. Semi-Supervised Driving Style Characterization

All driver inputs may not be accessible by electronic control systems.Certain variables, however, may construct an input-output pair that maybe used to deduce driver control structure. For example, during acar-following maneuver, the relative distance between the leading andfollowing car and the driver's braking and throttle requests are usuallywell coordinated. Here we consider using a Tagaki-Sugeno (TS) model torelate the variance of the driver's braking and throttling commands tothe relative range and velocity between the leading and following car.

A fuzzy system may utilize the signal conditioned mean driving headway(gap-time) relative to the other vehicle, as well as the standarddeviation of the rate changes of the accelerator pedal and brake pedalto determine whether the driver is aggressive or cautious. The driverindex value from fuzzy computation and rule evaluation may determine theaggressiveness of the driver based on car following, vehicle speed andthe driver's control actions on acceleration and deceleration.

For real-time vehicle implementation, the recursive estimation of themean and variance of a variable of interest is applied. The signalconditioned average mean gap-time at sample time k can be computed as

$\begin{matrix}{g_{k} = {g_{k - 1} + {\alpha \left( \frac{\Delta_{s_{k}}}{v_{fk} - g_{k - 1}} \right)}}} & (24)\end{matrix}$

where Δs_(k) is the relative distance between the leading and followingvehicle, and v_(fk) is the velocity of the following vehicle. α is afilter coefficient similar to the one used in (22). FIGS. 13A and 13Bshow the mean gap-times computed from two runs of vehicle testing: onefor aggressive driving and the other for cautious driving.

The acceleration pedal rate mean can be computed as

$\begin{matrix}{{\overset{\_}{\rho}}_{k} = {{\overset{\_}{\rho}}_{k - 1} + {\alpha \frac{\left( {\rho_{k} - \rho_{k - 1}} \right)}{{\Delta \; T} - {\overset{\_}{\rho}}_{k - 1}}}}} & (25)\end{matrix}$

where ρ is the acceleration pedal mean and ΔT is the sample time. Thecorresponding variance can be computed as

ν_(k)αν_(k−1)+(1−α)(ρ_(k)− ρ _(k))²  (26)

and the standard deviation is obtained from the square-root of thevariance. FIGS. 14A and 14B show the standard deviations of two runs oftest data for aggressive and cautious driving.

Similar to (25) and (26), the mean and variance of the brake pedal ratechange can be computed. FIGS. 15A and 15B show the standard deviationsof two runs of test data for aggressive and cautious driving. Thevariables are first normalized before presenting them to the fuzzyinference system. The fuzzy sets and membership functions weredetermined for the features to transform the crisp inputs into fuzzyterms. The mean gap-time fuzzy set G, is defined by

G _(s)={(g,μ(g))|gεG}  (27)

where G is given by the bounded collection of gap-times g in the vehiclepath. The gap-time membership function μ is chosen to be a Gaussianfunction.

A zero-order TS model was used to compute the driver index level. Anormalized output scale from 0-1.0 represented the levels from cautious,to less aggressive, to aggressive driving behavior. The driver index isobtained from fuzzy computation and rule evaluation. Table 1 shows therules used. Notice that a higher gap-time is relatively more safetyconscious compared to a lower gap-time.

TABLE 1 Rules for driving behavior characterization If accel If brake Ifgap-time pedal rate pedal rate Then driver is STD is STD is index is LowLow Low Less Aggressive High Low Low Cautious Low High Low AggressiveLow Low High Aggressive Low High High Aggressive High High High LessAggressive High Low High Cautious High High Low Less Aggressive

FIGS. 16A and 16B show the driver index computed from two runs ofvehicle testing data: one for aggressive driving with a driver indexgreater than 0.8 and the other for cautious driving with a driver indexless than 0.2.

VI. Supervised Driving Style Characterization

The car-following task requires the driver to maintain with the leadingvehicle one of the following (i) a zero speed difference; (ii) aconstant relative distance; and (iii) a constant relative gap-timedefined by the division of the relative distance by the relativevelocity.

A human driver may be modeled as a PD feedback controller. The closedloop system during a car following maneuver may be expressed as

({umlaut over (x)} _(l) −{umlaut over (x)} _(f) −{umlaut over ( x_(g))=−c _(v)({dot over (x)} _(l) −{dot over (x)} _(f) −{dot over ( x_(g))−c _(s)(x _(l) −x _(f) − x _(g))  (28)

where x_(l) and x_(f) are the leading and the following vehicle traveldistance and x _(g) is the gap offset reference. Due to theimplementation of radar used in vehicles equipped with adaptive cruisecontrol function, the relative distance and velocity are measured anddefined as

Δs=x _(l) −x _(f) , Δv={dot over (x)} _(l) −{dot over (x)} _(f)  (29)

A vehicle equipped with stability controls has a longitudinalaccelerometer with output α_(x), which measures {umlaut over (x)}_(f).(28) can be further expressed as

α_(x) =c _(v)(Δv−{dot over ( x _(g))+c _(s)(Δs−{dot over ( x_(g))+({umlaut over (x)} _(l) −{umlaut over ( x _(g))  (30)

The unknown parameters c_(v) and c_(s) in (30) can be used tocharacterize a driver's control structure during a car following. Usingthe low-pass filtered Δs and Δv to replace the gap offset reference v_(g) and its derivative {dot over ( v _(g), and considering the timedelays, we have the following equations

$\begin{matrix}{\alpha_{x_{k + i}} = {{{c_{v}\left\lbrack {{\Delta \; s_{k}} - {\mu_{k}\left( {\Delta \; s} \right)}} \right\rbrack} + {c_{s}\left\lbrack {{\Delta \; v_{k}} - {\mu_{k}\left( {\Delta \; v} \right)}} \right\rbrack} + {w\begin{bmatrix}{\mu_{k}\left( {\Delta \; s} \right)} \\{\mu_{k}\left( {\Delta \; v} \right)}\end{bmatrix}}} = {{\left( {1 - \alpha} \right)\begin{bmatrix}{\mu_{k - 1}\left( {\Delta \; s} \right)} \\{\mu_{k - 1}\left( {\Delta \; v} \right)}\end{bmatrix}} + {\alpha \begin{bmatrix}{\Delta \; s_{k}} \\{\Delta \; v_{k}}\end{bmatrix}}}}} & (31)\end{matrix}$

where subscript i in a α_(x) _(k+i) reflects the time delay between thedriver's braking/throttling actuation and the measured relative distanceand velocity, and acceleration, α is a low-pass filter coefficientsimilar to the one used in (22), and w is a high frequency uncertainsignal that may be treated as white noise. Using a conditional leastsquare identification algorithm, c_(v) and c_(s) can be identified inreal-time from (31). The response time t_(p) and the damping ratio ζ ofthe driver-in-the-loop system can be related to c_(v) and c_(s) as

t _(p)=2πc _(s)/√{square root over (4c _(s) −c _(c) ²)},ζ=c_(v)/2√{square root over (c _(s))}  (32)

which can be used to deduce the driver's driving behavior: (i) for anormal driver, it is desired that the transient response of thedriver-in-the-loop system be fast (sufficiently small t_(p), e.g., lessthan 0.5 s) and damped (sufficiently large ζ; (ii) for an aged or driverwith physical limitation, t_(p) may be large; (iii) for an aggressivedriver, ζ is likely to show a small value, such as one less than 0.5,and the system response is likely to exhibit excessive overshoot; (iv)for a cautious driver, ζ is likely to show a reasonably large value,such as one greater than 0.7.

A least-square parameter identification was implemented for calculatingc_(v) and c_(s). Two runs of vehicle testing were conducted. In the1^(st) run, the driver in the following car tried to use aggressivethrottling and braking to achieve a constant relative gap-time betweenhis vehicle and a leading vehicle, which led to larger range errorΔs_(k)−μ_(k)(Δs). See, FIG. 17. The identified c_(v) is around 0.2 andidentified c_(s) around 0.05. See, FIG. 18. The damping ratio thuscomputed from (32) showed a value less than 0.5, which is an indicationof a light damping driver-in-the-loop system, hence corresponding toaggressive driving behavior.

In the 2nd run, the driver was using cautious throttle and brakeapplication to achieve car following, the relative range errorΔs_(k)μ_(k)(Δs) in FIG. 19 had less magnitude in comparison with the oneshown in FIG. 17. The identified c_(v) and c_(s) are depicted in FIG.20. The damping ratio showed a value greater than 0.8 except during thefirst 150 seconds. See, FIG. 20. This is an indication of a heavydamping driver-in-the-loop system, hence corresponding to cautiousdriving behavior.

VII. Curve Over Speed Minder

Certain curve speed assistant technologies disclosed herein may use adigital map and/or navigation system to obtain upcoming road curvatureinformation to determine a curve speed limit based on, for example, thecurvature and acceptable curve lateral acceleration, and then issue awarning before entering the curve. The warning may be issued at somethreshold distance away from the road curvature and/or at some thresholdtime before entering the road curvature.

The upcoming road curvature may be determined in any known/suitable way.As an example, the curvature κ may be defined as the instantaneouschange of the unit vector tangent T with respect to the path of travel ssuch that

$\begin{matrix}{\kappa = \frac{T}{s}} & (33)\end{matrix}$

Thus, for an arc r=f(t)i+g(t)j with unit tangential vector i and unitnormal vector j, the components of the vector r are defined as functionsof time t as

x=f(t), y=g(t)

and the velocity vector is the derivative of the vector r as inv(t)=r′(t). The unit vector tangent to the path of travel can then becomputed

$\begin{matrix}{{T(t)} = {\frac{v(t)}{{v(t)}} = \frac{{f^{\prime}i} + {g^{\prime}j}}{\left( {{f^{\prime 2}i} + {g^{\prime 2}j}} \right)^{\frac{1}{2}}}}} & (34)\end{matrix}$

where f′ is the derivative of f. Using the chain rule on (33) yields

$\begin{matrix}{{\frac{T}{s} = {\frac{T}{t}\frac{t}{s}}}{where}{\frac{t}{s} = \frac{1}{{v(t)}}}} & (35)\end{matrix}$

The expression for κ is now

$\begin{matrix}{{\kappa (t)} = \frac{T^{\prime}(t)}{{v(t)}}} & (36)\end{matrix}$

and for the magnitude of curvature

$\begin{matrix}{{\kappa (t)} = {\frac{T^{\prime}(t)}{{v(t)}}}} & (37)\end{matrix}$

Starting with (34) and letting A=f′²+g′² yields

$T = {\frac{f^{\prime}i}{A^{\frac{1}{2}}} + \frac{g^{\prime}j}{A^{\frac{1}{2}}}}$

Taking T′(t) yields

$\begin{matrix}\begin{matrix}{{T^{\prime}(t)} = {\frac{}{t}\left\lbrack {\frac{1}{\sqrt{A}}\left( {{f^{\prime}i} + {g^{\prime}j}} \right)} \right\rbrack}} \\{= {{\frac{1}{\sqrt{A}}\left( {{f^{''}i} + {g^{''}j}} \right)} - {\frac{1}{2\; A\sqrt{A}}\left( {{2\; f^{\prime}f^{''}} + {2g^{\prime}g^{''}}} \right)\left( {{f^{\prime}i} + {g^{\prime}j}} \right)}}} \\{{T^{\prime}(t)} = \frac{{\left( {{g^{\prime 2}f^{''}} - {g^{\prime}g^{''}f^{\prime}}} \right)i} + {\left( {{f^{\prime 2}g^{''}} - {f^{\prime}f^{''}g^{\prime}}} \right)j}}{A\sqrt{A}}}\end{matrix} & (38)\end{matrix}$

and substituting (38) into (37) along with |v(t)|=√{square root over(A)} yields

$\begin{matrix}\begin{matrix}{{\kappa (t)} = {{\frac{T^{\prime}(t)}{{v(t)}}} = \left\lbrack \frac{{\left( {{g^{\prime 2}f^{''}} - {g^{\prime}g^{''}f^{\prime}}} \right)^{2}i} + {\left( {{f^{\prime 2}g^{''}} - {f^{\prime}f^{''}g^{\prime}}} \right)^{2}j}}{A^{4}} \right\rbrack^{\frac{1}{2}}}} \\{= {\frac{1}{A^{2}}\begin{bmatrix}{\left( {{g^{\prime 4}f^{''2}} - {2\; g^{\prime 2}f^{''}g^{\prime}g^{''}f^{\prime}} + {g^{\prime 2}g^{''2}f^{\prime 2}}} \right) +} \\\left( {{f^{\prime 4}g^{''2}} - {2\; f^{\prime 2}g^{''}f^{\prime}f^{''}g^{\prime}} + {f^{\prime 2}f^{''2}g^{\prime 2}}} \right)\end{bmatrix}}^{\frac{1}{2}}} \\{{{\kappa (t)} = {\frac{1}{A^{2}}\begin{bmatrix}{{g^{\prime 2}\left( {{g^{\prime 2}f^{''2}} - {2\; f^{''}g^{\prime}g^{''}f^{\prime}} + {g^{''2}f^{\prime 2}}} \right)} +} \\{f^{\prime 2}\left( {{f^{\prime 2}g^{''2}} - {2\; g^{''}f^{\prime}f^{''}g^{\prime}} + {f^{''2}g^{\prime 2}}} \right)}\end{bmatrix}}}}\end{matrix} & (39)\end{matrix}$

Note that the t parameter was left out of the right hand side forclutter considerations. Collecting terms, and substituting A=f′²+g′²back into (39) yields

${\kappa (t)} = \frac{\left\lbrack {\left( {f^{\prime 2} + g^{\prime 2}} \right)\left( {{g^{\prime 2}f^{''2}} - {2\; f^{\prime}f^{''}g^{\prime}g^{''}} + {f^{\prime 2}g^{''2}}} \right)} \right\rbrack^{\frac{1}{2}}}{\left( {f^{\prime 2} + g^{\prime 2}} \right)^{2}}$

Canceling common terms and noticing that

g′ ² f″ ²−2f′f″g′g″+f′ ² g″ ²=(g′f″−f′g″)²

we have the desired final form for curvature

$\begin{matrix}{{\kappa (t)} = \frac{{{g^{\prime}(t)}{f^{''}(t)}} - {{f^{\prime}(t)}{g^{''}(t)}}}{\left( {{f^{\prime 2}(t)} + {g^{\prime 2}(t)}} \right)^{\frac{3}{2}}}} & (40)\end{matrix}$

Thus for twice-differentiable functions f(t) and g(t), it is possible toconstruct a vector of curvature magnitude values for each t. As such,curvature has units of 1/length with length typically in meters. κ isoften inverted to form the radius of curvature with units of meters.(Radius of curvature is directly found next.)

A circle can be exactly fit between three non-collinear points P₁, P₂,and P₃ such that

(x−h)²+(y−k)² =r ²  (41)

where h and k form the coordinates of the circle center with radius r(radius of curvature 1/κ) as shown in FIG. 21. The geometric approach of(41) allows a curvature calculation for any orientation of the circle inthe xy plane.

The solution for the radius involves calculation of the (h,k) pair, anddetermining the length from (h,k) to one of the points P. Translatingthe coordinate system from xy to x′y′ using P₁ as the origin of the x′y′frame such that x′=x−x₁ and y′=y−y₁ changes (41) to

(x′−h′)²+(y′−k′)² =r ²  (42)

where h′=h−x₁ and C=k−y₁. The relocated origin could also have been P₂or P₃, but P₁ was used in this case as it relates to the vehicleposition being the origin of the local vehicle coordinate system.

Substituting p, P₂, and P₃ into (42) yields

h′ ² +k′ ² −r ²=0

(x′ ₂ −h′)²+(y′ ₂ −k′)−r ²=0

(x′ ₃ −h′)²+(y′ ₃ −k′)−r ²=0  (43)

where x′₂=x₂−x₁ and x′₃=x₃−x₁. Expanding the last two expressions in(43) yields

x′ ₂ ²−2x′x ₂ h′+h′ ² +y ₂ ²−2y′ ₂ k′+k′ ² −r ²=0

x′ ₃ ²−2x′x ₃ h′+h′ ² +y ₃ ²−2y′ ₃ k′+k′ ² −r ²=0

and eliminating h′², k′² and r² by subtraction with the first expressionin (43) yields

x′ ₂ ²−2x′ ₂ h′+y′ ₂ ²−2y′ ₂ k′=0

x′ ₃ ²−2x′ ₃ h′+y′ ₃ ²−2y′ ₃ k′=0

which can now be solved for h′ and k′ such that

$\begin{matrix}{\begin{Bmatrix}h^{\prime} \\k^{\prime}\end{Bmatrix} = {\begin{bmatrix}{2\; x_{2}^{\prime}} & {2\; y_{2}^{\prime}} \\{2\; x_{3}^{\prime}} & {2\; y_{3}^{\prime}}\end{bmatrix}^{- 1}\begin{Bmatrix}{x_{2}^{\prime 2} + y_{2}^{\prime 2}} \\{x_{3}^{\prime 2} + y_{3}^{\prime 2}}\end{Bmatrix}}} & (45)\end{matrix}$

Finally, the radius of curvature ρ is calculated from

ρ=√{square root over (h′ ² +k′ ²)}  (46)

With

h=h′+x ₁

k=k′+y ₁  (47)

Radius of curvature ρ may be thought of, in certain circumstances, asthe radius of a curve assuming that the curve radius is reasonablyconstant.

A typical scenario is shown in FIG. 22. In this scenario, a vehicle isapproaching a curve with radius ρ. The curvature profile shown in theinset reflects a curve with a transition section where radius ofcurvature changes from zero to ρ. The transition does not always existin real roads with the radius of curvature change being discontinuousfrom zero to ρ.

The pentagon and circular markers in FIG. 22 represent map databasecoordinates (from a known navigation system for example) that representthe road. Certain map databases for production navigation systems mayrepresent the road to approximately ±15 m in an absolute sense. Therelative accuracy may be better, however, and support radius ofcurvature accuracy within 10% of actual.

A target vehicle speed based on the curvature profile may be determinedfrom a map database. A basic curve speed determination may be given by

v_(ρ)=√{square root over (a_(lat)ρ)}  (48)

where v_(p) is the speed, and a_(lat) is the target maximum lateralacceleration in the curve. a_(lat) values may be centered around 2m/s²(0.2 g) and depend on vehicle type/testing. Another formulation thattakes into account the expected side friction and superelevation is

$\begin{matrix}{v_{\max}^{2} = {\rho_{\min}{g\left( {\frac{e_{\max}}{100} + f_{\max}} \right)}}} & (49)\end{matrix}$

where f_(max) is a dimensionless side friction factor, and e_(max) isthe superelevation in percent. Superelevation is also known as roadbank, and is defined as the tangent of the bank angle. As can be seen in(49), the

$g\left( {\frac{e_{\max}}{100} + f_{\max}} \right)$

term is an expansion of a_(lat) in (48). So, rather than assuming ageneric lateral acceleration, it is possible to incorporate informationrelating to side friction and superelevation using (49). In certainimplementations, road friction may be estimated from the vehicle ABS orESC system using known techniques, and superelevation information may,for example, be extracted using known techniques from map databases orcomputations using sensors equipped with electronic controls.

In some embodiments, a threshold distance (at which to issue awarning/alert) from the curve may be determined by a selectable constantdeceleration profile. The deceleration profile may be selected based onthe driver categorization/characterization discussed above. Table 2shows example deceleration profiles for various drivercategorizations/characterizations (of course, other decelerationprofiles are also possible)

TABLE 2 Driver categorization/characterization versus decelerationDriver Type Deceleration Expert 3.0 m/s² Cautious 2.0 m/s² Reckless 1.0m/s²From basic kinematics, the distance required to change speed from thecurrent vehicle speed to the curve speed under constant deceleration canbe determined by

$\begin{matrix}{d_{decel} = \frac{v_{\rho}^{2} - v_{x}^{2}}{2\; a_{lon}}} & (50)\end{matrix}$

where d_(decel) is the deceleration distance required to slow thevehicle from the current speed v_(x) (which may be determined in anyknown/suitable fashion such as wheel speed sensors, the referencevelocity computed in ESC, etc.) to v_(ρ) over the selected longitudinalacceleration (negative for deceleration) a_(lon). By comparing currentvehicle position along the road, as determined by the navigation system,with the d_(decel) distance before the curve, a warning is issued if thevehicle distance to the curve becomes less than d_(decel). Usingdifferent values of a_(lon) as discussed above allows differentd_(decel) thresholds to be established.

In other embodiments, a threshold warning distance from the curve may bedirectly selected based on the driver categorization/characterizationdiscussed above. Table 3, for example, shows example threshold distancesfor various driver categorizations/characterizations (other thresholddistances are also possible)

TABLE 3 Driver categorization/characterization versus distance DriverThreshold Type Distance Expert 30 m Novice 45 m Reckless 70 mOnce a threshold warning distance has been selected based on drivertype, an alert/warning may be generated if the current vehicle speed isgreater than the target curve speed and the distance from the vehicle tothe curve is less than the threshold distance.

In still other embodiments, a threshold warning time from entering thecurve may be selected based on the drivercategorization/characterization discussed above. Table 4, for example,shows example threshold times for various drivercategorizations/characterizations (other threshold times are alsopossible)

TABLE 4 Driver categorization/characterization versus time DriverThreshold Type Time Advanced 1.5 sec Average 3 sec Beginner 4 secOnce a threshold warning time has been selected based on driver type, analert/warning may be generated if the current vehicle speed is greaterthan the target curve speed and the time to enter the curve, T_(curve),is less than the threshold time. The time to enter the curve, T_(curve),may, of course, be based on the current vehicle speed, v_(x), and thecurrent distance from the curve, d_(current)

$\begin{matrix}{T_{curve} = \frac{d_{current}}{v_{x}}} & (51)\end{matrix}$

Alternatively, a vehicle that is within some threshold distance (thatdoes not depend on driver type) of a road curvature may be issuedwarnings/alerts depending on the driver type and current vehicle speed.For example, once a vehicle is less than 70 meters away from a roadcurvature, an alert may be generated if the vehicle speed is greaterthan the target curve speed based on the driver type: if the driver isfound to be “expert,” for example, an alert will not be generated unlessthe current vehicle speed is more than 10 mph above the target curvespeed; if the driver is found to be “reckless,” for example, an alertwill not be generated unless the current vehicle speed is more than 2mph above the target curve speed, etc. Other scenarios are alsopossible.

In yet still other embodiments, a default deceleration profile,threshold distance, and/or threshold time (depending on theconfiguration) may instead be altered based on the drivercharacterization/categorization. For example, if a driver type is foundto be “average,” the default threshold value may be used. If the drivertype is found to be “expert,” the default threshold value may be alteredby some percentage (e.g., a default deceleration profile may beincreased by 30%, a default threshold time may be decreased by 20%,etc.)

Referring to FIG. 23, an embodiment of a driver advisory system 30 for avehicle 32 may include a speed sensor 34, one or more controllers 36, anavigation system 38, and an audio, visual and/or haptic interface 40.The speed sensor 34 detects a speed associated with the vehicle 32. Theinterface 40 may be any suitable/known driver interface such as adisplay screen, speaker arrangement, haptic accelerator pedal, hapticseat, etc.

The one or more controllers 36 may receive vehicle speed informationfrom the sensor 34, road information from the navigation system 38, andinformation described above and used to categorize/characterize adriver's dynamic control of the vehicle 32 in any suitable/known fashion(via, for example, a car area network). Using the algorithms discussedabove, the one or more controllers 36 may categorize a driver's dynamiccontrol of the vehicle 32 by type, select a threshold warning distance,time and/or acceleration, determine a target curve speed (if the vehicle32 is approaching a curve), determine whether a current speed of thevehicle 32 is greater than the target curve speed, and determine whetherthe current distance or time is less than the threshold. If thepreceding conditions are met, the one or more controllers 36 maygenerate an alert/warning for the interface 40. For example, the one ormore controllers 36 may activate the interface 36 if the interface is ahaptic interface. The system of FIG. 1 may be similarly configured.Other arrangements are also possible.

VIII. Intersection Minder

Alerts or warnings may also be generated in a manner similar to thatdescribed with reference to the curve over speed minder as the vehicle32 approaches a road intersection where the vehicle 32 must stop (based,at least in part, on information commonly available from the navigationsystem 38). Such an intersection minder, however, need not determineroad curvature or a target curve speed as described above because thetarget vehicle speed when arriving at the intersection is assumed to bezero (i.e., full stop). Because the target vehicle speed is zero, theintersection minder also need not determine whether the current vehiclespeed is greater than the target vehicle speed.

Once the one or more controllers 36 characterize/categorize the driver'scontrol of the vehicle 32, the one or more controllers 36 may select anacceleration, distance, time, etc. as described above. (If a thresholdacceleration is selected, a corresponding threshold distance may bedetermined via (50) setting v_(ρ) equal to zero.) Warnings/alerts maythen be generated as discussed above if for example, the distance awayfrom the intersection is less than the threshold distance or if the timeto the intersection is less than the threshold time.

As apparent to those of ordinary skill, the algorithms disclosed hereinmay be deliverable to a processing device, which may include anyexisting electronic control unit or dedicated electronic control unit,in many forms including, but not limited to, information permanentlystored on non-writable storage media such as ROM devices and informationalterably stored on writeable storage media such as floppy disks,magnetic tapes, CDs, RAM devices, and other magnetic and optical media.The algorithms may also be implemented in a software executable object.Alternatively, the algorithms may be embodied in whole or in part usingsuitable hardware components, such as Application Specific IntegratedCircuits (ASICs), state machines, controllers or other hardwarecomponents or devices, or a combination of hardware, software andfirmware components.

While embodiments of the invention have been illustrated and described,it is not intended that these embodiments illustrate and describe allpossible forms of the invention. The words used in the specification arewords of description rather than limitation, and it is understood thatvarious changes may be made without departing from the spirit and scopeof the invention.

1. A method for advising a driver of a vehicle comprising: categorizingthe driver's dynamic control of the vehicle by type; determining atarget speed of a road curvature; determining a speed of the vehicle;determining a threshold distance based on the type; determining adistance between the vehicle and the curvature; and generating an alertfor the driver if the distance is less than the threshold and the speedis greater than the target.
 2. The method of claim 1 whereincategorizing a driver's dynamic control of the vehicle by type includesmeasuring a plurality of parameters representing the vehicle's currenthandling condition and the vehicle's limit handling condition anddetermining a margin between the vehicle's current handling conditionand limit handling condition, and wherein the driver's dynamic controlof the vehicle is categorized by type based on the margin.
 3. The methodof claim 1 wherein categorizing a driver's dynamic control of thevehicle by type includes monitoring driver torque requests, establishingtypes of driver behavior based on a history of driver torque requestsand associated rates of change thereof, and assigning current driverbehavior into one of the established types based on current drivertorque requests and associated rates of change thereof.
 4. The method ofclaim 1 wherein the vehicle includes an accelerator pedal and a brakepedal each having positions, wherein categorizing a driver's dynamiccontrol of the vehicle by type includes determining a gap time betweenthe vehicle and another vehicle, determining a variability of a rate ofchange of at least one of the accelerator and brake pedal positions, andwherein the driver's dynamic control of the vehicle is categorized bytype based on the gap time and the variability of the rate of change. 5.The method of claim 1 wherein categorizing a driver's dynamic control ofthe vehicle by type includes determining a distance and relative speedbetween the vehicle and another vehicle and measuring a longitudinalacceleration of the vehicle, and wherein the driver's dynamic control ofthe vehicle is categorized by type based on the distance and relativespeed between the vehicles and the longitudinal acceleration of thevehicle.
 6. The method of claim 1 wherein the vehicle includes a hapticdriver interface and wherein generating an alert for the driver if thedistance is less than the threshold and the speed is greater than thetarget includes activating the haptic driver interface.
 7. The method ofclaim 1 wherein determining a threshold distance based on the typeincludes selecting a target deceleration based on the type.
 8. Themethod of claim 1 wherein the threshold distance is further based on thespeed of the vehicle.
 9. The method of claim 1 wherein the thresholddistance is further based on the target speed of the road curvature. 10.A vehicle comprising: a driver interface; and at least one controlleroperatively arranged with the interface and configured to categorize adriver's dynamic control of the vehicle by type, to determine a targetspeed of a road curvature, to determine a speed of the vehicle, todetermine a threshold time based on the type, to determine a time untilthe vehicle enters the road curvature, and to generate an alert for thedriver via the interface if the time is less than the threshold and thespeed is greater than the target.
 11. The vehicle of claim 10 whereinthe interface is a haptic driver interface.
 12. A method of advising adriver of a vehicle comprising: categorizing the driver's dynamiccontrol of the vehicle by type; determining a threshold distance basedon the type; determining a distance between the vehicle and a roadintersection; and generating an alert for the driver if the distance isless than the threshold distance.
 13. The method of claim 12 whereincategorizing a driver's dynamic control of the vehicle by type includesmeasuring a plurality of parameters representing the vehicle's currenthandling condition and the vehicle's limit handling condition anddetermining a margin between the vehicle's current handling conditionand limit handling condition, and wherein the driver's dynamic controlof the vehicle is categorized by type based on the margin.
 14. Themethod of claim 12 wherein categorizing a driver's dynamic control ofthe vehicle by type includes monitoring driver torque requests,establishing types of driver behavior based on a history of drivertorque requests and associated rates of change thereof, and assigningcurrent driver behavior into one of the established types based oncurrent driver torque requests and associated rates of change thereof.15. The method of claim 12 wherein the vehicle includes an acceleratorpedal and a brake pedal each having positions, wherein categorizing adriver's dynamic control of the vehicle by type includes determining agap time between the vehicle and another vehicle, determining avariability of a rate of change of at least one of the accelerator andbrake pedal positions, and wherein the driver's dynamic control of thevehicle is categorized by type based on the gap time and the variabilityof the rate of change.
 16. The method of claim 12 wherein categorizing adriver's dynamic control of the vehicle by type includes determining adistance and relative speed between the vehicle and another vehicle andmeasuring a longitudinal acceleration of the vehicle, and wherein thedriver's dynamic control of the vehicle is categorized by type based onthe distance and relative speed between the vehicles and thelongitudinal acceleration of the vehicle.
 17. The method of claim 12wherein the vehicle includes a haptic driver interface and whereingenerating an alert for the driver if the distance is less than thethreshold distance includes activating the haptic driver interface. 18.The method of claim 12 wherein determining a threshold distance based onthe type includes selecting a target deceleration based on the type. 19.A vehicle comprising: a driver interface; at least one controlleroperatively arranged with the interface and configured to categorize adriver's dynamic control of the vehicle by type, to determine athreshold time based on the type, to determine a time until the vehicleenters a road intersection, and to generate an alert for the driver viathe interface if the time is less than the threshold.
 20. A method foradvising a driver of a vehicle comprising: categorizing the driver'sdynamic control of the vehicle by type; determining a target speed of aroad curvature; determining a speed of the vehicle; determining adistance between the vehicle and the curvature; determining an alertcondition based on the type, target speed, speed, and a thresholddistance; and generating an alert in response to the alert condition.